3.4

Is It A Right Triangle?

Pg. 13Pythagorean Theorem Converse and Distance

3.4 – Is It A Right Triangle?_______________Pythagorean Theorem Converse and Distance

In lesson 3.3, you learned how to use the Pythagorean Theorem. Today you are going to use this information to find the length between two points on a graph. You are also going to determine if the triangle is acute, right, or obtuse.

3.24 – DISTANCEUse the Pythagorean theorem to find the following.

A

B

7

3

d

49 + 9 = d2

58 = d2

l2 + l 2 =h2

58 =d

72 + 32 = d2

b. A(-6, 2)and B(-2, -3)

A

B

5

4

d16 + 25 = d2

41 = d2

l2 + l 2 =h2

41 =d

42 + 52 = d2

c. A(-1, 2)and B(3, 4)

A

B2

4

x

4 + 16 = d2

20 = d2

l2 + l 2 =h2

2 5 =d

22 + 42 = d2

Distance Formula:

x2 – x1

y2 – y1

2 2 2x y d

3.25 – DISTANCE FORMULAFind the distance between the two points. Simplify your square roots.

a. A(2, 4)and B(8, 19)

2 2 2x y d 62 + 152 = d2

36 + 225 = d2

261 = d2

d = 3 29

b. A(-2, 3)and B(-8, 6)

2 2 2x y d 62 + 32 = d2

36 + 9 = d2

45 = d2

d = 3 5

c. A(-5, 2)and B(-2, -7)

2 2 2x y d 32 + 92 = d2

9 + 81 = d2

90 = d2

d = 3 10

3.26 – WHAT'S THE PATTERN?Use the tools you have developed to find the lengths of the missing sides of the triangles below. If you know a shortcut, share it with your team. Look for any patterns in the triangles as you solve. Are any triangles similar and multiples of others? Keep answers in exact form.

2 2 23 4x

5

2 2 26 8x

10

2 2 23000 4000x

5000

2 2 213 5x

12

2 2 226 10x

24

2 2 2130 50x

120

        

 

3.27 – PYTHAGOREAN TRIPLES

4

3

512

5

13

3.28 – EXTRA PRACTICEFind the area of the shapes using Pythagorean triples to help find the missing sides.

8

3

4

triangle rectangleA 1

2

A bh bh

1 4 3

2A 8 3

6A 24 230un

81

2A bh

136 8

2A

2144A un

5

530

30 20

20

A = 100un2

Right TriangleAcute

TriangleObtuse Triangle

        

   

b

a

c

2 2 2c a b

b

a

c

2 2 2c a b

b

a

c

2 2 2c a b

3.29 – TRIANGLE CLASSIFICATIONFor each set of numbers, determine if the triangle is acute, right, or obtuse. SHOW WORK!

a. 8, 15, 17

2 2 217 8 15 289 64 225

289 289

ACUTE, RIGHT, or OBTUSE

b. 3, 5, 7

2 2 27 3 5 49 9 25 49 34

ACUTE, RIGHT, or OBTUSE

c. 8, 10, 12

2 2 212 8 10 144 64 100 144 164

ACUTE, RIGHT, or OBTUSE

d.

ACUTE, RIGHT, or OBTUSE

22 289 5 8

89 25 64 89 89

e.

22 28 5 3 7

64 25 63 64 88

ACUTE, RIGHT, or OBTUSE

f.

22 212 2 10 9

144 40 81 144 121

ACUTE, RIGHT, or OBTUSE